Commutator Length of Leaf Preserving Diffeomorphisms

被引:1
作者
Fukui, Kazuhiko [1 ]
机构
[1] Kyoto Sangyo Univ, Dept Math, Kyoto 6038555, Japan
基金
日本学术振兴会;
关键词
commutator length; leaf preserving diffeomorphism; uniformly perfect;
D O I
10.2977/PRIMS/83
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the group of leaf preserving C-infinity-diffeomorphisms for a C-infinity-foliation on a manifold which are isotopic to the identity through leaf preserving C-infinity-diffeomorphisms with compact support. We show that for a one-dimensional C-infinity-foliation F on the torus, this group is uniformly perfect if and only if F has no compact leaves. Moreover we consider the group of leaf preserving C-infinity-diffeomorphisms for the product foliation on S-1 x S-n which are isotopic to the identity through leaf preserving C-infinity-diffeomorphisms. Here the product foliation has leaves of the form {pt} x S-n. We show that this group is uniformly perfect for n >= 2.
引用
收藏
页码:615 / 622
页数:8
相关论文
共 17 条
[1]   COMMUTATORS OF EQUIVARIANT DIFFEOMORPHISMS [J].
ABE, K ;
FUKUI, K .
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1978, 54 (02) :52-54
[2]  
Abe K, PREPRINT
[3]   Commutators of C∞-diffeomorphisms preserving a submanifold [J].
Abe, Kojun ;
Fukui, Kazuhiko .
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2009, 61 (02) :427-436
[4]   The first homology of the group of equivariant diffeomorphisms and its applications [J].
Abe, Kojun ;
Fukui, Kazuhiko .
JOURNAL OF TOPOLOGY, 2008, 1 (02) :461-476
[5]  
Banyaga A., 1997, The Structure of Classical Diffeomorphism Groups, V400
[6]  
Denjoy A., 1932, Journal de Mathematiques Pures et Appliques, V11, P333
[7]   Commutators and diffeomorphisms of surfaces [J].
Gambaudo, JM ;
Ghys, T .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2004, 24 :1591-1617
[8]  
HERMAN MR, 1971, CR ACAD SCI A MATH, V273, P232
[9]   COMMUTATORS OF DIFFEOMORPHISMS .3. A GROUP WHICH IS NOT PERFECT [J].
MATHER, JN .
COMMENTARII MATHEMATICI HELVETICI, 1985, 60 (01) :122-124
[10]   COMMUTATORS OF DIFFEOMORPHISMS .2. [J].
MATHER, JN .
COMMENTARII MATHEMATICI HELVETICI, 1975, 50 (01) :33-40